Rauschenbach's
Theory of Perspective and Photography Is a 50mm lens still a good choice?
_______________________________________________________

"
viewers usually do not carry rulers around."
B.V. Rauschenbach. General Theory of Perspective

Introduction

Boris
Rauschenbach is a well-known Russian scientist and engineer who stood
behind many space exploration projects. Also he spent a lot of time to
investigate the peculiarities of perspective. He studied many works by
famous artists to understand how depth and distance can be shown on a
flat surface. As a result, he amended the classical theory of perspective
that was discovered during the renaissance. As far back as 1986, he wrote
a fundamental book entitled The Systems of Perspective in Art. General
Theory of Perspective, in which he described his ideas from both mathematical
and aesthetical points of view. As far as I know, this book has not been
translated into English so far. In this brief article, I would like to
popularize his ideas among English-speaking audience and to apply his
theory to photography.

Of
course, within such a small text I cannot explain the entire theory to
you. You will find neither mathematical formulas, nor scientific problems
here. I would like to keep things simple and give you just some basic
information.

You
should also keep in mind that visual perception is a very complex subject.
To understand it, we must know how brain processes information, how our
eyes form images, as well as many other related issues. This article does
not deal with visual perception directly. It just explains some facts
connected with the perception of space.

The classical approach

Any
general purpose photographic lens renders images in accordance with the
classical linear theory of perspective. Thus, first of all we have to
understand methods of the classical theory of art.

The
picture below can be found in many books on art. It shows how a room with
the dimensions of 4 by 5 yards and three men in it can be shown on a flat
surface of a picture.

a.
The artist is too close to the pictorial plane. In photography this
case is related to wide angle lenses. The room looks deeper than
its natural depth. The window looks too wide. All the three men
can easily stand near it, if necessary.

b.
and c. The distance between the artist and the pictorial plane is
as recommended in many text-books. The depth is close to natural.
In 35mm photography, this case corresponds to the use of normal
lenses (ca. 50mm).

d.
The remote artist looks at the picture at a narrow angle. The room
looks as if it were only 2 yards deep instead of 4 yards. The image
is flatter. The window looks too narrow. According to our perception,
only one person can stand near it.

All
four cases represent the perspective of the room correctly. Still, the
impression is different. A 50mm lens is considered as normal because it
produces most natural perception of depth.

Unfortunately,
many people are firmly convinced that all lenses reproduce perspective
in the same way. Their reasoning is simple. They suggest
taking several pictures with the help of various lenses while
standing on the same spot. If we allow for the natural differences in content,
we will see that perspective will be practically the same in all such
photos. With the help of the same arguments, they demonstrate that
perspective cannot depend on the size of the film frame (or digital
sensor). “If we simply cut out the central part of the frame,
why should its perspective change?” they ask. But when saying
this, they just demonstrate that they do not understand the kernel
of the problem. Both the focal distance of a lens and the size of the
film frame affect the perspective through the same mechanism, namely
through the change of the distance between the camera and the foreground.
To see the changes in perspective, a photographer has to move closer
to (or farther from) the foreground in order to allow the foreground
to fill the same share of the image. When
we say that different lenses show perspective differently, we imply
that we have to change the distance between the camera and foreground
to make an adjustment for the changed viewing
angle. Only
under such a condition, perspective will be completely determined by
the
viewing angle of the “lens
plus frame” system. The picture above demostrates exactly this case.

However
some specialists,
including Rauschenbach, say it is a rough approach. Thus, let us consider
the subtle details.

What
is wrong with the classical theory?

Actually
among the properties of the visual perception there is such an important
thing like constancy. The constancy can be of shape, of color,
and of size. Due to the constancy of size, our perception makes
close objects smaller, and distant objects larger. According to the theory,
for any object and circumstances, there is the optimal distance of natural
visual perception.

The
photographs taken with a 35mm lens often show distant mountains as unnaturally
small parts of the image. At the same time, very close items are shown
as huge objects. This can be corrected a little, if we switch to a 50mm
lens. It will produce a more natural image as far as the mountains are
concerned. They will be enlarged and rendered closer. However, the 50mm
lens will fail to decrease the size of the items in the foreground. Thus,
there are no lenses with natural perspective. All of them are unnatural
to a certain extent, and a photographers task is to minimize deviations
from the natural visual perception.

Similarity,
scale, and depth

According
to Rauschenbach, there are three main parameters that must be shown correctly
in a picture. Those are similarity, scale, and depth.

The
following example demonstrates how to treat all of them. Suppose we have
to show two identical triangles in our picture. Also suppose we know the
distances at which both triangles are located. Of course, the distant
triangle should be smaller. The question is  what are the other
rules for us to follow?

1. The correct similarity means a1 / b1
= a2 / b2. All general purpose photographic lenses
are designed to comply with this requirement.

2.
The correct scale means a1 / a2 = b1
/ b2. According to Rauschenbach, there is the optimal scale
to show our triangles in a picture. This optimal scale corresponds to
the most natural perception of scales in the image. Actually, this optimum
depends on many factors, but we will not discuss such things in this
article.
A photographer can select the necessary scale by using a lens with the
appropriate focal length.

3.
The correct depth means we must select the optimal ratio a1
/ d. Again, Rauschenbachs theory states that such an optimum exists
and produces most natural perception of depth in a picture. Again, a
photographer can select the necessary level of depth by using a lens
with the appropriate focal length.

The
classical theory treats all such things in a similar way, but it does
not take into account the fact that the correct scale optimum does not
coincide with the correct depth optimum. The corresponding errors cannot
be minimized simultaneously. If we minimize depth errors, the scale errors
will remain big enough, and vice versa. This is a fundamental difference
between Rauschenbachs approach and the classical theory of perspective.

To
a photographer, this means there is no universal focal length. The lenses
should be chosen depending on the particular purposes and situations.
Still, some lenses are more universal than the others. The explanation
to this will be given below.

The
law of conservation of distortion

This
is another crucial point in the general theory of perspective. According
to this law, the sum of all representation errors (errors of similarity,
scale, and depth) remains constant in all reasonable cases. When the law
does not hold, the cumulative error is unusually large.

In
photography, the law holds for the lenses with focal lengths of 24mm to
150mm, according to my personal estimations. It does not mean other lenses
cannot be used to produce decent images. Even an unnatural perspective
can be very artistic!

This
law is very important for practical purposes, because it says there is
always a tradeoff between similarity, scale, and depth. It is a photographers
task to choose what is important and what is not.

Main
types of perspective

Rauschenbachs
main types of perspective are described in the table below. Actually,
the optimal observation distance L depends on the object size, its surroundings
and many other factors as well. It is even different for the width and
height. However, such subtle deviations are not taken into account in
this text.

Type
A (the renaissance linear perspective). Only similarity is shown
without distortion. It corresponds to the case when objects are
observed from the optimal distance L.
The foreground is significantly enlarged, while the background is
unnaturally small. The depth is slightly exaggerated.

In
35mm photography, this type of perspective corresponds to the lenses
with focal lengths of 24mm to 35 mm.

Type
B. The linear perspective as observed from the distance of 2L.
It naturally renders similarity and depth (especially for vertical
elements). Like the renaissance perspective, it does not show scales
naturally.

In
35mm photography, this type of perspective corresponds to the lenses
with focal lengths of 50mm to 70 mm.

Type
C. One can obtain this type of linear perspective, when the
pictorial plane is located at the distance of 4L.
Scales are rendered without errors. Like any other linear perspective,
similarity is also shown naturally. Depth is distorted, the image
looks somewhat flat.

In
35mm photography, this type of perspective corresponds to the lenses
with focal lengths of 100mm to 135mm (so-called portrait lenses).

Type
D. It is an example of how painters can give up similarity to
produce natural perception of depth and scale on horizontal surfaces.
Scales for the verticals are rendered unnaturally.

This
type of perspective cannot be obtained in photography.

Type
E.It
is an example of how painters can give up similarity to produce
natural perception of depth and scale on vertical surfaces. Scales
for the horizontals are rendered unnaturally.

This
type of perspective cannot be obtained in photography.

Those
were only the main types of perspective. You may create your own scheme
if necessary.

In
his book, Rauschenbach said nothing about focal distances. I draw the
analogy based on my experience and common sense. Of course, it is not
exact. If you are unhappy with it, develop your own conformity approach.
Here I just want to demonstrate some general ideas to you.

The
main recommendation for photographers

The
variety of perspective types demonstrates that there cannot be the universal
focal distance in photography. Each time a photographer wants to take
a shot, he should choose the optimal focal distance that corresponds to
his tasks and circumstances. One should also avoid composing frames with
the help of zooming. Once the suitable focal length is selected, it is
always better to change the composition by changing the distance to the
object.

The
50mm prime lens is still the best!

Both
classical books on art and Rauschenbachs theory agree that painters and
photographers prefer to show natural depth in their pictures. This task
corresponds to Type B in the table, i.e. to a 50mm lens.

As
I said above, a 50mm lens is also good for landscapes, because it shows
natural depth from the middle area to the background. Of course, close
objects are distorted. But one can easily arrange such a composition that
minimizes errors of scale. Even close portraits can be made with such
a lens. The example of a natural close shot made with a 50mm lens can
be found at the end of this article.

Wide-angle
and super telephoto lenses

Now
that you know the general principles, you may be astonished at the fact
that super telephoto lenses are capable of showing objects naturally.

It
is easy to demonstrate mathematically that small objects can be naturally
shown in an axonometric system. Many painters do use it in practice. Only
under such conditions, super telephoto lenses can show objects naturally.
One should apply them for other purposes with great care.

The
same can be said about wide-angle lenses. They cannot render natural perspective.
Like telephoto lenses, they should be used only if the photographer deals
with the special artistic task or cannot use any other lens in the given
circumstances.

Is
it a good theory to follow?

Any
scientific theory has its limitations and drawbacks. It does not mean
theories are bad. When applying them, you should only remember to observe
a number of conditions. As far as art and photography are concerned, your
taste and common sense can also assist you a lot.

Please
also look at four my photos that I selected to illustrate this article.
Only one of them complies with the requirements of the theory. Feel free
to draw your own conclusions.

Example
1. Cityscape made with a telephoto lens

This
example demonstrates how a telephoto lens compresses the depth of the
image. The grey building looks unnaturally close to the trees. Actually,
it is located on the other bank of the river and is 400 meters away from
us. The building in the background also looks too close to us (it is located
at the distance of 2.5 km).
According to Rauschenbachs theory, both scales and depth are shown unnaturally
here. I agree with that. I just wanted to show architectural objects here.
In my opinion, it was not important to comply with the natural perception
rules in such cases.

Example
2. Cityscape made with a 50mm prime lens

This
shot complies with all the recommendation. Both scales and depth are shown
naturally. The only drawback of a 50mm lens in this case is a slightly
unnatural rendering of the water surface of the river. Of course, your
opinion may not coincide with both my words and the theory.

Example
3. Sketch of a boy made with a telephoto lens

It
would have been better to take this shot with a lens with a slightly wider
angle of view. The boy looks a little bit flat. Only blurred pavement
shows the depth of the picture. However, scales are natural, and the proportions
are perfect.

When
taking this shot, I had no control over the situation. I also could not
move closer in order not to attract the boys attention.

Example
4. Portrait made with a 50mm lens

This
picture contradicts both classical recommendations and Rauschenbachs
theory. Still, I consider it rather a good image. I did my best to arrange
such a composition, when natural perception of scales was not important.
Moreover, the portrait obtained natural depth. I admit it is not a masterpiece
but quite a decent picture.

The
example shows that any theory and any recommendations must be applied
with care. Under special circumstances, a 50mm prime lens can be a good
portrait lens.